City were among the teams to avoid for those finishing first in their groups and Group H winners Barca arguably drew the short straw at a ceremony held in Nyon.
The Catalan giants are leading the Primera Division and scoring freely despite the absence of star striker Lionel Messi but Manuel Pellegrini's men are in particularly formidable form in the Barclays Premier League having recently put seven goals past Norwich, six past Tottenham and six past Arsenal.
City also stunned European champions Bayern Munich by winning 3-2 at the Allianz Arena last week, a feat which did not go unnoticed by Barca boss Martino.
He told AS: "They are scoring goals freely and I don't want to experience that first hand.
"We want to play well through the knockout stages and, of course, win all our games.
"We have to see what state other teams are in when we get to February. I won't rush into making an analysis now.
"But they are an important rival and have very good players."
"You hope for the best during the draw and then you just have to deal with what comes out of it.
"Maybe the other side didn't want to be drawn against Barca."
City's director of football Txiki Begiristain - formerly of Barcelona - said the team is brimming with confidence.
He told the club's website: "I think it will be a great match.
"Ours is a team with a lot of confidence especially after winning against the champions in Munich - that will give us a lot of confidence. Not just at home but away as well.
"We are showing that we can score in all matches. This is important in the Champions League.
"We scored in Plzen, in Moscow, in Munich - it should give us confidence to play against a team who have been champions many times.
"Our manager (Pellegrini) knows perfectly Barcelona because he managed in Spain for a long time. In this sense, we are confident."